Growth and characterization of two dimensional carbon nanostructures

GROWTH AND CHARACTERIZATION OF TWO
DIMENSIONAL CARBON NANOSTRUCTURES













WANG HAOMIN

NATIONAL UNIVERSITY OF SINGAPORE

2009

GROWTH AND CHARACTERIZATION OF TWO
DIMENSIONAL CARBON NANOSTRUCTURES








WANG HAOMIN
(B. Eng., M. Eng., Huazhong University of Science and Technology, P. R.
China)

A THESIS SUBMITTED
FOR THE DEGREE OF DOCTOR OF PHILOSOPHY
DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING
NATIONAL UNIVERSITY OF SINGAPORE
2009
Acknowledgements
National University of Singapore i

ACKNOWLEDGEMENTS

The work in this thesis could not have been accomplished without the
contribution of guidance, support and friendship of many people.
First of all, great gratitude should be extended to my supervisor, Professor Wu
Yihong, for his valuable guidance and helpful technical support throughout my PhD
study. Had it not been for his advice, direction, patience and encouragement, this thesis
would certainly not be possible. Not only his serious attitude towards research but also
his courage to face difficulties makes a great impact on me.
I am grateful to my co-supervisor, A/P Teo Kie Leong for his kind help and
encouragement over the entire course of my Ph. D project.
I am glad that I have so many considerate and supportive labmates. I bother
them whenever I want: Dr. Yang Binjun helped me with the MPECVD system and
SEM observations in the beginning of my research study; Mr. Liu Tie imparted me his
experimental skills in photo/e-beam lithography, the cryostat system and electrical
characterization; Ms. Ji Rong let me know how to use Raman spectrometer in DSI; Mr.
Tsan Jing Ming assisted me in the CNWs growth experiments; Ms. Delaram Abedi
helped me in the Raman characterization on CNWs; Mr. Chen Junhao helped me in the
low temperature measurement on CNW devices; Mr. Teo Guoquan conducted the
simulation on visibility study of graphene in multilayered structure; Mr. Xiong Feng set

up the lock-in measurement system and helped conduct electrical characterization on
graphene devices at low temperature; Dr. Ni Zhenhua and Ms. Wang Yingying helped
me in the Raman and contrast characterization on grapheme flakes; Prof. Shen Zhexiang
and Dr. Yu Ting allowed us to use their Raman spectrometer in NTU; Dr. Zhao
Acknowledgements
National University of Singapore ii
Zheliang and Dr. Wang Junzhong maintained the cryostat system in good condition; Ms.
Naganivetha Thiyagarajah was willing to show me her techniques in using E-beam
lithography system; Dr. Sunny Lua and Dr. Li Hongliang shared their experience in e-
beam evaporator; Dr. Han Gang showed me how to operate the mini-sputtering system;
Special thanks go to Ms. Catherine Choong who has helped conduct the laborious low-
temperature measurement on most of my CNW devices.
Sincere thanks should also go to all the staff in both Information Storage and
Materials Laboratory (ISML) of the National University of Singapore (NUS) and Data
Storage Institute (DSI). They are true professionals. They have been important for
smooth experiments for the users. They have helped me in one way or another in my
studies and daily life. I also want to acknowledge the excellent experimental and study
environment provided by both NUS and DSI.
I am indebted to other fellow group members. Working with Mr. Liu Wei, Dr.
Maureen Tay, Dr. K. S. Sunil, and Mr. Saidur Rahman Bakaul, has been a lot of fun.
Their friendship and happy time spent with them throughout four years of studies. I am
also grateful to everyone else of my friends for their deep concern and enthusiastic
support. Sharing with them the joy and frustration has made my life fruitful and
complete.
The scholarship provided by the National University of Singapore for my PhD is
gratefully acknowledged. Lastly but most importantly, I deeply am thankful for the
continuous care and support of my family throughout my whole course of study.


Table of contents

National University of Singapore iii

TABLE OF CONTENTS

Acknowledgements i
Table of contents iii
Abstract viii
List of tables x
List of figures xi
Nomenclature xxiv
Acronyms xxviii
List of publications 226

Chapter 1 Introduction 1
1.1 Carbon-based Nanostructures of Different Dimensionality 2
1.2 Energy Band Structure of Two Dimensional Carbon 5
1.3 Carbon Nanowalls – Disordered 2D Carbon 8
1.3.1 Fabrication of Carbon Nanowalls 8
1.3.2 Structure and Morphology 11
1.3.2 Transport
Properties of Carbon Nanowalls 13
1.4 Graphene - 2D carbon of high perfection 17
1.4.1 Fabrication of Graphene 18
1.4.2 Electrical Properties of Graphene 21
1.5 Motivation 22
1.6 Objectives 24
1.7 Organization of this thesis 26
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National University of Singapore iv
Chapter 2 Graphene Under Modification

35
2.1 Introduction 35
2.2 Bilayer and Multilayer Graphene 36
2.3 Carbon Nanoribbon: Electronic Confinement and Edge State 39
2.4 Graphene Nanoflake or Nanodot 46
2.5 Graphene Functionalization 49
2.6 Extrinsic Graphene 52
2.7 Summary 55

Chapter 3 Experimental Details
72
3.1 Growth of Carbon Nanowalls 72
3.1.1 Substrate Preparation 72
3.1.2 MPECVD 73
3.1.3 Growth Conditions 75
3.2 Characterization of Carbon Nanowalls (SEM, TEM, Raman
Spectroscopy)
75
3.3 Fabrication of Carbon Nanowalls Devices 77
3.4 Fabrication of Graphene 79
3.5 Selection of Graphene Flakes (Methods of Raman and
Optical contrast)
81
3.6 Fabrication of Graphene Based Devices 85
3.7 Method to Fabricate Graphene Devices on Different
Substrates
86
3.8 Electrical Characteristic Setup 94

Chapter 4 Electronic Transport Properties of Carbon

Nanowalls Using Normal Metal Electrodes
99
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4.1 Introduction 99
4.2 Mesoscopic Transport in Two Dimensional Carbon 99
4.3 Temperature Dependence of Carbon Nanowalls Network
Structure
101
4.4 Semiconductor-like Behavior of Carbon Nanowalls Sheets 105
4.5 Differential Conductance Fluctuation 109
4.6 Giant Gap-like Behavior of Differential Conductance 115
4.7 Magnetic Field Dependence of Electronic Transport
Properties
120
4.8 Conclusion 125


Chapter 5 Electronic Transport Properties of Carbon
Nanowalls Using Superconducting Electrodes
132
5.1 Introduction 132
5.2 Superconductivity 132
5.3.1 Josephson Effect 134
5.3.2 Andreev reflection 135
5.3.3 Multiple Andreev Reflections 136
5.3.4 Possible Superconductivity in Graphitic Materials 137
5.3 Sample Fabrication and Experimental Details 138
5.4 Temperature Dependence of Resistance in Nb/CNWs/Nb 139
5.5 Electrode Spacing Effect 141

5.6 Transparency at Nb/CNWs Interface 142
5.7 Temperature-dependence of Differential
Resistance/Conductance
145
5.7.1 Zero Bias Resistance (ZBR) 145
5.7.2 Critical Current 147
5.7.3 Multiple Andreev Reflection 153
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5.8 Magnetoelectrical Transport Properties 158
5.8.1 Zero Bias Resistance 158
5.8.2 Critical current 159
5.8.3 Multiple Andreev Reflection 161
5.9 Conclusion 164

Chapter 6 Electronic Transport in Graphene and Its Few
layers on Silicon Dioxide Substrates
170
6.1 Introduction 170
6.2 Electrical Field Effect in Graphene and its Multilayers 171
6.2.1 Electrical Field Effect 171
6.2.2 Carrier Mobility 174
6.2.3 Minimal Conductivity 176
6.3 Hysteresis in Graphene Devices 178
6.3.1 Charge Transfer Hysteresis 179
6.3.2 Capacitive Gating Hysteresis 185
6.4 Magneto Transport Study at Low Temperature 189
6.4.1 Four-layer Graphene Device 189
6.4.2 Monolayer Graphene Device 193
6.5 Conductance Fluctuation at Low Temperature 198

6.5.1 Four-layer Graphene 200
6.5.2 Monolayer Graphene Device 202
6.5.3 Bilayer Graphene Device 205
6.5.4 Summary 212
6.6 Conclusion 213

Table of contents
National University of Singapore vii
Chapter 7 Conclusions and recommendation for future work
220
7.1 Conclusions 220
7.2 Recommendation for future work 223



Abstract
National University of Singapore viii
ABSTRACT
This dissertation focuses on the electronic transport properties of carbon
nanowalls and graphene flakes. The former has been carried out by using both normal
metal (Ti) and superconductor (Nb) electrodes. Bottom electrodes are employed in the
experiments. Comparing to top-electrode configuration, this configuration could help
to narrow the electrode spacing of devices down below 1 μm.
In the Ti/CNW/Ti junctions, the experimental results show the presence of a
narrow band gap and conductance fluctuations within a certain temperature range.
Excess conductance fluctuations observed between 4 and 300 K are attributed to the
quantum interference effect under the influence of thermally induced carrier excitation
across a narrow bandgap. The sharp suppression of conductance fluctuation below 2.1
K is accounted for by the formation of a layer of He 4 superfluid on the nanowalls. The
results obtained here have important implications for potential application of CNWs in

electronic devices. A giant gap-like behavior of dI/dV is also observed in some
samples. The gap indicates that some phase transition may happen in those CNWs at
low temperature.
For Nb/CNW/Nb junctions, superconducting proximity effect was observed in
two samples with short electrode spacing. Their temperature dependence of critical
current is in good agreement with both Josephson coupling in long diffusive model and
Ginzburg-Landau relationship. The above-gap feature and Andrev reflection were
observed in the two samples. Their magnetic field dependence was also discussed.
However, in other Nb/CNWs/Nb devices, results of proximity effect with respect to
the electrode spacing are not consistent. This may be due to many reasons, such as the
orientation of CNWs, quality of CNW sheet, the transparency of Nb/CNWs interface.
Abstract
National University of Singapore ix
In the second part of this thesis, we discuss the electric transport properties of
graphene on SiO
2
substrate with different number of layer under ambient condition. By
examining carrier mobility, minimal conductivity and conductance hysteresis in
graphene devices, it is found that the substrate interface and surface impurity may
greatly affect the transport properties of graphene on SiO
2
substrate. Our experimental
results indicate that magneto transport and conductance fluctuation in graphene
devices are greatly affected by the charged impurities at the substrate/graphene
interface.
List of tables
National University of Singapore x

LIST OF TABLES

Table 1.1 Literature review about the research work on fabrication of
CNWs by CVD method
9
Table 5.1 Electronic parameters of carbon nanowalls sandwiched between
Nb electrodes with an electrode gap of 300nm at 1.4K. Values
are derived from the parameters given by van Schaijk et al.
Fermi velocity, , is taken to be 1x106m/s, ħ and kB refers to
the Plank constant and Boltzmann constant respectively.
149
Table 5.2 Principle characteristics of the superconducting junctions obtain
with CNWs. a
1
and a
2
are the fitting parameters in SNS junction
agreement with the long junction limit. D is the diffusive
coefficient deduced from (5.6) and
mfp
L is the mean free path
deduced from (5.6). Fitting R
N
is is the normal state resistance
deduced from formula (5.7). E
c
is the Thouless energy deduced
from
2
/ LDE
c
h= .

151
Table 5.3 Principal features of the superconducting junctions obtains with
CNWs. T
c
is the transition temperature of the Nb/CNWs/Nb
junction.,
c
I is the critical current of the junction and R
N
is the
normal state resistance.
J
E is the Josephson coupling energy
estimated from
c
I . eV is charging energy at
c
I . TK
B
is the
thermal energy under 1.4K.
153
Table 5.4 Principle fitting features of the superconducting junctions of
CNWs. “low” and “high” means the low magnetic field and
high magnetic field region.
164

List of figures
National University of Singapore xi
LIST OF FIGURES

FIG. 1.1 The carbon family (adapted from EE5209 lecture notes by
Prof. Wu Yihong)

3
FIG. 1.2 Graphene and its reciprocal lattice. a) Lattice structure of
graphene,
1
a
v
and
2
a
v
are the lattice vectors. There are two
carbon atom (A and B) in one unit cell (shaded area). b) The
reciprocal lattice of graphene defined by
1
g
v
and
2
g
v
. The
corresponding first Brillouin zone is depicted as the shaded
hexagonal. The Dirac cones located at K and K’ points.

5
FIG. 1.3 Electronic energy band structure of graphene. The valence
band (lower band) and the conduction band (upper band).

Right: magnification of the energy bands close to one of the
Dirac point, showing the energy dispersion relation is linear.

7
FIG. 1.4 SEM ((a) and (b)) and HRTEM ((c) and (d)) images of carbon
nanowalls. Scale bars: (a) 100 nm, (b) 1 µm, (c) and (d) 5 nm.
(a) was taken at a tilt angle of 25o. (Refer to Ref. 15).

12
FIG. 1.5 Temperature dependence of the resistance of the carbon
nanowalls at low temperature at zero-field and a field of 400
Oe. Inset is the temperature dependence of the resistance over
a wider temperature range. Also shown is the first derivative of
the resistance with respect to the temperature. (Refer to Ref.
[15])

14
FIG. 1.6 Magnetoresistance curves of the carbon nanowalls measured at
different temperatures (a), and enlarged portion of the curve at
4.31 K (b). The inset of (b) is the Fourier transform spectrum
of the entire curve at 4.31 K shown in (a). (Refer to Ref. [15])

16



FIG. 1.7 a) Optical image of a few-layer graphene sheet and schematic
view of a graphene device. Figures from Ref.[17]. b)
Nanopencil used to extract few layer graphene flakes from

19
List of figures
National University of Singapore xii
HOPG. (Figures from Ref. [63]). c) AFM image of a few layer
graphene quantum dot fabricated by dispersion from solution.
(Figures adapted from Figures from Ref.[66]). d) Growing
graphene layers on SiC. (Figures from Ref.[16]).
FIG. 1.8 a) The conductivity of monolayer of graphene vs. gate voltage.
b) The Quantum Hall Effect in single layer graphene. (Figures
taken from Ref.[18])

22



FIG. 2.1 The 2D primitive cells of few layer graphene with different
stacking orders. (Refer to Ref. [30])

37
FIG. 2.2 Details of few layer graphene band structures in the vicinity of
K point and near the Fermi level (always set as zero), noting
that the bands of the ABAC 4-layers are not crossing and a gap
is open. (Refer to Ref. [30])

37
FIG. 2.3 (a) Lattice structure of a bilayer graphene with Bernal
stacking. The A and B sublattices are indicated by white and
red spheres, respectively. (b) Band structure of bilayer
graphene near the Dirac points for V=150meV (solid line) and
V=0 (dashed line).(Refer to Ref. [17]) (c) Schematic

illustration of a graphene bilayer excitonic condensate channel
in which two monolayer graphene sheets are separated by a
dielectric barrier. The electron and hole carriers induced by an
external electrical field will form a high temperature excitonic
condensate. (d) The two band model indicated by solid lines,
the two remote bands indicated by dashed lines. (Refer to Ref.
[25])

38
FIG. 2.4 Two types of edge shape for graphene ribbons: (a) zigzag edge
and (b) armchair edge. The edges are indicated by the hold
lines. The red and blue circles show the A and B site carbon
atoms, respectively; (c) the relationship of energy gap and the
width N in armchair ribbon, whose 2/3 show the
semiconducting gap. (Figures adapted from K. Wakabayashi,

40
List of figures
National University of Singapore xiii
2003)
FIG. 2.5 (a) Atomic force microscope (AFM) and scanning electron
microscope (SEM) images of GNRs fabricated by plasma
etching, and the relationship between conduction gap and the
width of GNR (refer to Ref.[57]). (b) Atomic force microscope
(AFM) image of chemically derived GNRs down to sub-10 nm
width, and the relationship between conduction gap and the
width of GNRs. (Refer to Ref.[58])

41
FIG. 2.6 (a) The wavenumber dependence of the populations of the

edge state; (b) the energy dispersions of nanographene ribbon
having zigzag edges with a width of 30 unit cells; (c) the
density of states, and (d) Ferromagnetic spin arrangement at
the zigzag edges. All the edge carbon atoms are terminated
with hydrogen atoms. (Refer to Ref.[42])

44
FIG. 2.7 (a) An atomically resolved UHV STM image of zigzag and
armchair edges (9×9nm2) observed in constant height mode
with bias voltage Vs= 0.02 V and current I = 0.7 nA. (b) The
dI/dV curve from STS data at a zigzag edge. (c) A dI/dV curve
from STS measurements taken at an armchair edge. (Refer to
Ref.[69])

45
FIG. 2.8 Various types of graphene nanoflakes stitched up from smaller
subflakes (darker shade). Black lines are stitches, and the
hydrogen termination along the edges is not shown. (Refer to
Ref.[87])

46
FIG. 2.9 (a) Scaling of spin and energy gap with the inverse linear size
(1/n) of zigzag-edged triangular graphene flakes. (b) Zigzag-
edged triangular graphene flakes with ferrimagnetic order and
linearly scaling net spin. (c) An example of a GNF attached to
a GNR, forming a possible spintronic component. (Refer to
Ref.[87])

47
FIG. 2.10 (a) STM topograph and (b) topographic spatial derivative of a

5nm (lower feature) and 2nm wide (upper) feature single layer

48
List of figures
National University of Singapore xiv
graphene pieces. Log(I)-V spectra plotted as a function of
position for the (c) 5nm and (d) 2nm wide graphene
monolayers, (e) Energy gap (Eg) vs width of GNF (L) in 10
semiconducting graphene nanoflakes, which follows the
relationship: Eg (eV)=1.57± 0.21 eV nm/L1.19± 0.15. (Refer
to Ref. [96] and [97])
FIG. 2.11 Schematics of crystal structure of (a) graphene and (b)
graphane, where blue (red) spheres represent the carbon
(hydrogen) atoms. (c) A derivative model: one side
hydrogenated region is adjoined by two non-hydrogenated
ones. (d) Schematic band diagrams for the three regions shown
in (c). The diagrams are positioned under the corresponding
graphene regions. Hydrogenated regions are represented by a
gapped spectrum whereas the non-hydrogenated regions are
assumed to be gapless. The ellipsoids inside the gap represent
localized states. (Refer to Ref.[117])

51
FIG. 2.12 (a) Sketch of the geometry considered for the study of a single
B-site vacancy. (b) Comparison between the local DOS in the
vicinity of a vacancy (blue/solid) with the bulk DOS (red/
dashed) in clean systems. (c) Total DOS in the vicinity of the
Dirac points for clusters with 4x106 sites, at selected vacancy
concentrations. (Refer to Ref. [129])

53
FIG. 2.13 (a) Atomic resolution STM image 6×6 nm2, a single graphene
on SiO2. (b) Atomic resolution STM image 20×20 nm2,
irradiated graphene on SiO2, defect sites are indicated by
arrows. (c) Scanning tunneling spectra of graphene taken on
the defect free region and a defect site of the irradiated
graphene. (Refer to Ref. [140]).

54
FIG. 2.14 Schematic illustration of electronic properties in graphene
under various modifications. The possible electronic properties
are summarized below the dashed line.

56



List of figures
National University of Singapore xv
FIG. 3.1 Schematic diagram of MPECVD setup. The reactant gases
flow through the flowing meters and through the quartz
chamber. The microwave generates plasma in the chamber,
where the carbon nanowalls grow.

74
FIG. 3.2 (a) SEM image of CNWs. Dotted lines represent the electrodes
configuration; (b) HRTEM image of CNWs; (c) Raman
spectrum of CNWs.

76

FIG. 3.3 SEM images of (a) bottom electrode configuration, scale bar
corresponds to 10 µm. and (b) a close-up view of electrodes
showing current flow and voltage probes, scale bar
corresponds to 1 µm.

78
FIG. 3.4 (a) Schematic illustration of the electrodes before CNWs
deposition. Current is passed and voltage is measured across
the junction as indicated by the arrows. CNWs are deposited in
the region encompassed by the dotted lines; (b) Schematic
diagram of cross-sectional structure of the metal/CNWs/metal
device after CNWs deposition. The electrodes are separated by
a gap of “d” which varies between 300 nm and 1µm.

79
FIG. 3.5 (a) The graphite crystal and scotch tape; (b) The scotch tape
used to exfoliate graphite. (c) Optical microscope image of
thin graphite flake before and (d) after applying metallic
electrodes. (Scale bar corresponds to 8µm)

80
FIG. 3.6 Raman spectra of graphite and graphene with different number
of layers.

83
FIG. 3.7 The contrast spectra of graphene sheets with different number
of layers.

83
FIG. 3.8 (a) The optical image of a graphene sample with 1 to 4 layers

(Scale bar corresponds to 8µm); (b) The 3D contrast image,
which shows a better perspective view of the sample.

84
FIG. 3.9 Schematic of lithography for the electrode fabrication process.

85
List of figures
National University of Singapore xvi
FIG. 3.10 A multilayer model used in the transfer matrix simulation.

87
FIG. 3.11 (a) Schematic of structure for a graphene sheet on top of a Si
substrate capped with SiO
2
thickness ranging from 0 to
400nm. (b) Optical contrast spectra of monolayer graphene on
SiO
2
/Si substrate as a function of wavelength from 400 nm to
750 nm with variable SiO
2
thickness. (c) Schematic of
structure for a graphene sheet on a layer of PMMA coated on
top of a Si substrate with 300nm SiO
2
. (d) Optical contrast
spectra of SLG on PMMA/SiO
2
/Si substrate as a function of

wavelength from 400 nm to 750 nm with PMMA thickness
ranging from 0 to 200nm on top of a SiO
2
(300nm) coated Si
substrate.(e) Calculated contrast of graphene as a function of
wavelength from 400 nm to 750 nm and PMMA thickness of
top layer from 0 to 300 nm for the structure of SLG
sandwiched between two PMMA layers on top of a
SiO
2
(300nm) coated Si substrate. (f) Corresponding contrast
spectra for the schematic described in (e).

90
FIG. 3.12 a) Schematic of structure for a graphene sheet on a layer of
100nm PMMA placed on top of Si substrate with 300nm SiO
2
.
b) An optical image of monolayer graphene on
PMMA(100nm)/SiO
2
(300nm)/Si. The outline areas
correspond to SLG, the scale bar is 20μm. c) Experimental
results of contrast spectra of the graphene sample, d) Raman
spectrum of the monolayer graphene flake. The position of G
peak and the spectral features of the 2D band confirm the
number of the layers.

92
FIG. 3.13 Fabrication process for a free standing graphene device.

93
FIG. 3.14 A sample in chip carrier for measurement

94
FIG. 3.15 An optical image of a graphene device with basic electrical
setup in our investigations. The Fermi level in the graphene
and the perpendicular electric field are controllable by means
of the voltages applied to the back gate, V
bg
. We study the

95
List of figures
National University of Singapore xvii
resistivity of the graphene flake as a function of gate voltage
by applying a current bias (I ) and measuring the resulting
voltage (V) across the device.
FIG. 3.16 Electrical measurement setup. A DC or AC current was
applied to the sample while LabVIEW program was used to
sweep the magnetic field (B) or electrical field (E) and to
measure the voltage (
x
V or
y
V ) passing across the sample.

96

FIG. 4.1
(a) Temperature dependence of resistance (
)/exp(~ TR Δ )
behavior in one CNWs sample is observed at
KT 15
<
, where
Δ
is a constant . Inset: the same data but for the low
temperature interval (
TR
~
) behavior is observed at
KT 15> ); (b) Temperature dependence of resistance
(
)/exp(~ TR Δ behavior is observed in another CNWs sample
with top electrodes at
KT 20
<
, where
Δ
is a constant . Inset:
the same data but for the low temperature interval
(
)/exp(~
3/1
0
TTR ) behavior is observed at KT 20> , where
0

T
is a constant. The sample dimensions are given in µm and
the current is shown as an arrow. The red lines are guides for
the eye.

103
FIG. 4.2
(a) Temperature dependence of resistance ( )/exp(~
TR Δ )
behavior is observed at
KT 5
<
in one CNWs sample with
bottom electrodes, where
Δ
is a constant. Inset: the same data
but for the high temperature interval ( )~
TR behavior is
observed at
KT 50> ; (b) Temperature dependence of
resistance (
)/exp(~ TR
Δ
) behavior is observed at KT 5< in
another CNWs sample with bottom electrodes, where
Δ is a
constant. Inset: the same data but for the high temperature
interval (
T
R

~
) behavior is observed at KT 70> . The sample
dimensions are given in µm and the current is shown as an
arrow. The red lines are guides for the eye.

104
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National University of Singapore xviii
FIG. 4.3 Plot of zero bias resistance versus temperature for four Ti/
CNWs/Ti samples with an electrode spacing of 300 nm
(circle), 450 nm (square), 800 nm (upward triangle) and 1 μm
(downward triangle), respectively. Dashed-lines are fits with
the STB model.

108
FIG. 4.4 The differential conductance of (a)-(b) 300nm sample; (c)-(d)
450nm sample, plotted as a function of applied voltage at
different temperature.

110
FIG. 4.5 The differential conductance of (a)-(b) 800nm sample and (c)-
(d) 1μm sample, plotted as a function of applied voltage V for
different temperature range.

111
FIG. 4.6 A plot of rms[δG] vs. T for the four Ti/Carbon nanowalls/Ti
samples. Insert: temperature dependence of rms[δG] for the
four samples at low temperature.

113

FIG. 4.7 Differential conductance curves at temperatures (a) decreasing
and (b) increasing from 1.4 K to 2.5 K plotted as a function of
applied bias voltage V for the sample with an electrode
spacing of 1µm.

116
FIG. 4.8 Plot of zero bias resistance versus temperature in Figure 4.7.

117
FIG. 4.9 Magnetoresistance behaviour of (a-b) 300 nm, (c-d) 450 nm
and (e-f) 800 nm samples at 1.4 K and 2.5 K respectively.

123
FIG. 4.10 A plot of root mean square of differential conductance
fluctuation vs Magnetic field for the three Ti/Carbon
nanowalls/Ti samples from 0T to 6T with a sweep of 0.5T per
step at 1.4K and 1.5K respectively. The magnetic field was
applied perpendicular to the substrate surface.

124



FIG. 5.1 Schematic illustration of Andreev reflection at N/S interface.
An electron in the normal electrode with energy (E<Δ) pairs
with another electron with opposite energy and wave vector to

135
List of figures
National University of Singapore xix

form a cooper pair in the superconductor. The result is a hole
(open circle) in N with opposite energy and equal wave vector
reflected away from the interface. Adapted from Ref. [11].
FIG. 5.2 a)-c) Schematic illustration of multiple Andreev reflection
processes at different bias voltages. In d), the contribution to
the current of the processes in (a-c) is indicated.

137
FIG. 5.3 Temperature dependence of zero bias resistance (ZBR) for
samples of various electrode gaps.

140
FIG. 5.4 The normalized conductance of an SNS calculated with BTK
theory with various values of Z. The arrows indicated the trend
with increasing Z from 0 to 1.5 with an interval of 0.25.

143
FIG. 5.5 The temperature dependence of differential conductance of
(a)185nm, (b) 243nm, (c)387nm and (d) 702nm.

144
FIG. 5.6 The differential resistance vs current of the Nb/CNWs/Nb
junction with a gap width of (a) 239nm and (b) 429nm under
different temperature.

146
FIG. 5.7 (a) Temperature dependence of critical current, I
c
, and zero
bias resistance (ZBR) of the 239nm and 429nm samples

indicated by symbols. The dotted lines represent the
theoretical fit from Josephson coupling energy model. (b)
Temperature dependence of I
c
fitted with Ginzburg Landau
relationship.

148
FIG. 5.8 dI/dV and IV curve as a function of bias Voltage at 1.4K of (a)
239nm sample and (b) 429nm sample.

155
FIG. 5.9 Differential resistance vs voltage of (a) 239nm and (b) 429nm
sample under different temperature.


156
FIG. 5.10 Temperature dependence of the peaks indicated in Figure 5.8.
(a) Sample 239nm, (b) 429nm. The solid and dashed lines
display the temperature dependence of Δ(T) which
corresponding to different critical temperature T
c
based on the
BCS theory.

157
List of figures
National University of Singapore xx
FIG. 5.11 Zero bias resistance as a function of magnetic field at 1.4 K.

158
FIG. 5.12 Differential resistance as a function of current and magnetic
field up to a maximum field of (a) 2T in the sample 239nm
and (b) 3T in the 429nm sample.

160
FIG. 5.13 Critical currents Ic as a function of the magnetic field under
1.4 K in sample 239nm and sample 429nm.

161
FIG. 5.14 Magnetic field dependence of differential resistance vs bias
voltage of (a) 239nm and (b) 429nm samples.

162
FIG. 5.15 (a) and (b) magnetic field dependence of the peaks indicated in
Figure 5.14; respectively; (d) and (c) Peak positions (symbols)
are fitted as a function of magnetic field, theoretical fitting
curve is derived from Eqs. (5.8) with different
superconducting gap in sample 239nm and 429nm sample.

163



FIG. 6.1 Electrical characterization of a trilayer graphene device. (a)
Conductance as a function of backgate voltage; Two- (red
line) and four probe (black line) conductance at room
temperature. The inset is optical images of the corresponding
devices. Contact numbers are used in the main text to explain
different geometries; (b) resistance versus gate voltage.

172
FIG. 6.2 Mean mobility as a function of the number of layers before
deposition of SiO
2
. The column represents the mean value of
the mobility of graphene sample. The error bar represents the
standard deviation of all the raw data. Solid circles represent
the raw data of mobility.

175
FIG. 6.3 Mean minimum conductivity per layer as a function of the
number of layers before a) and after b) deposition of SiO
2
. The
error bar represents the standard deviation of all the raw data.
The dashed lines are guide for eyes; c) column diagram for
comparison of data before and after the deposition of SiO
2
.

177
List of figures
National University of Singapore xxi
FIG. 6.4 a) Optical image of a BLG device (bs4q3p7) lying on SiO
2
; b)
Conductance vs gate voltage curves recorded under sweep rate
of 1.25 V/s in ambient condition. As the gate voltage is swept
from negative to positive and back a pronounced hysteresis is

observed, as indicated by the arrows denoting the sweeping
direction.

180
FIG. 6.5 a) Conductance hysteresis recorded under three different V
gate

sweep rates in ambient condition; b) Conductance vs gate
voltage curves recorded for the same device as in Figure 6.4
under three different gate voltage range in ambient condition;
Device hysteresis increases steadily with increasing voltage
range due to avalanche charge injection into charge traps; c)
Close up of (b) within the low voltage region; d) Diagram of
avalanche injection of holes into interface or bulk oxide traps
from the graphene FET channel.

181
FIG. 6.6 (a) Shift of the neutrality point as a function of the number of
layers. The error bar represents the standard deviation of all
the raw data. The dashed line is guide for eyes; (b) Two-point
conductance as a function of gate voltage in a bilayer sample
LF5 before and after the application of a large current in
helium gas atmosphere and at T=300 K.

184
FIG. 6.7 The carrier density in graphene is affected by two mechanism.
a) Transferring a charge carrier (hole) from graphene to charge
traps causes the right shift of conductance, and vise versa; b)
Capacitive gating occurs when the charged ion or polar alters
the local electrostatic potential around the graphene, which

pulls more opposite charges onto graphene from the contacts.
c) Schematics of hysteresis caused by the capacitive gating,
where the arrows denoting the sweeping direction; this kind of
hysteresis observed in some of our samples in helium vapor at
4.2K. (d) 4-layer graphene device (Bs4q3p8) and (e)
monolayer graphene device (Bs5q1p14) are representatives.

188
List of figures
National University of Singapore xxii
(The arrows denote the sweeping direction. the insets are
optical images of the corresponding devices, and graphene was
profiled between dashed lines).
FIG. 6.8 Gate electric field modulation of the magneto-resistance as a
function of magnetic field measured at T=4.2K in a 4 layer
graphene (bs4q3p8). Numbers near each curve indicate the
applied gate voltages. The inset shows an optical image of
the sample with measurement geometry.

190
FIG. 6.9 ΔR
xx
as a function of inverse magnetic field at (a) +50V,
(b)+25V, (c)-5V, (d)-25V and (e)-50V. ΔR
xx
obtained from the
measured R
xx
by subtracting a smooth background. Solid
(open) symbols correspond to peak (valley) of the oscillations.

(f) Landau plots (see text) obtained from (a)-(d). Lines are
linear fits to each set of points at different V
g
. Inset: the
frequency of the SdH oscillations obtained from the slopes of
the line fits in (f) as a function of gate voltage.

192
FIG. 6.10 Conductance as a function of gate voltage at T=4.2K (a)
B=0T, (b) B=6T for the four layer graphene sample (bs4q3p8).

193
FIG. 6.11 Gate electric field modulation of the magneto-resistance as a
function of magnetic field measured at T=1.4K in a monolayer
graphene (bs5q1p14). Numbers near each curve indicate the
applied gate voltages. The inset shows an optical image of the
sample with measurement geometry.

194
FIG. 6.12 ΔR
xx
as a function of inverse magnetic field at (a) +50V,
(b)+25V, (c) 0V, (d)-25V and (e)-50V. ΔRxx obtained from
the measured ΔRxx in Figure 6.11 by subtracting a smooth
background. (f) Illustration of ideal cases for Δ Rxx as a
function of inverse magnetic field in monolayer graphene and
its few-layer.

196
FIG. 6.13 Conductance as a function of gate voltage at T=4.2K (a)

B=0T, (b) B=6T for monolayer graphene sample.

197
List of figures
National University of Singapore xxiii
FIG. 6.14 (a) The back gate voltage dependence of conductivity for a 4
layer graphene device (inset: the sample geometry and
measurement configuration. The boundary of graphene is
denoted by a dashed line.); (b) The gate voltage dependence of
resistance for the same sample; (c) the ΔG vs gate voltage at
1.4K and 60K;(d) the ΔR vs gate voltage at 1.4K and 60K.

202
FIG. 6.15 (a) Conductance vs gate voltage for a monolayer graphene
device (inset: the sample geometry and measurement
configuration. The boundary of graphene is denoted by a
dashed line.); (b) The gate voltage dependence of resistance
for the same sample; (c) the ΔG vs gate voltage at different
temperatures from 1.4K to 300K, (the traces at different
temperature were successively added with 0.04e^2/h except
1.47K for clarity.) (d) the ΔR vs gate voltage at different
temperature.

204
FIG. 6.16 (a) Conductance vs gate voltage for bilayer graphene device
(inset: the sample geometry. The boundary of graphene is
denoted by a dashed line.); (b) The gate voltage dependence of
resistance for the same sample; (c) the ΔG vs gate voltage at
different temperatures from 1.4K to 300K;(d) the ΔR vs gate
voltage at different temperature.

207
FIG. 6.17 a) Differential conductance fluctuation at gate bias from -80V
to 80V plotted as a function of duration time for the bilayer
graphene at 1.4K; b) Rms[ΔG] versus gate voltage at 1.4 K,
4.23K, 54.45K for the bilayer graphene; c) Bottom of
conduction band ε+ , top of valance band ε- and Fermi level
E
F
as the function of carrier density n (bottom axis) and V
g

(top) in a biased bilayer graphene with top p type doping
(3.81×10
12
cm
-2
), d) the relationship of E
F
– E
D
vs n and gate
voltege in bilayer and monolayer graphene. The Fermi energy
goes up much faster with charge density in the monolayer.

208